cosmological constant

cosmological constant
Value	~1.1056×10−52 m−2
Units	m−2
Dimension	L−2

cosmological constant is a fundamental constant in Albert Einstein's general relativity that represents a uniform energy density filling space homogeneously. Introduced by Einstein in 1917 to allow for a static universe, it was later abandoned after Edwin Hubble's discovery of the expansion of the universe. In modern physical cosmology, it is the leading candidate to explain the observed accelerated expansion of the universe, often associated with the energy of the vacuum state in quantum field theory.

Introduction

The term appears in the Einstein field equations as an additional term proportional to the metric tensor (general relativity). This modification allows solutions to the equations that describe a universe which is neither expanding nor contracting, a concept that appealed to the prevailing static universe model of the early 20th century. Its physical interpretation has evolved significantly, with contemporary Lambda-CDM model identifying it as the simplest form of dark energy responsible for the universe's accelerating expansion. The value of this constant is extraordinarily small yet non-zero, a fact that presents one of the deepest puzzles in theoretical physics.

Historical development

Albert Einstein first introduced the concept in 1917 while applying his general relativity to the structure of the universe as a whole. He sought a solution that would describe a static universe, which was the dominant cosmological model before the work of Alexander Friedmann and Georges Lemaître. Following Edwin Hubble's observations at the Mount Wilson Observatory demonstrating the recessional velocity of galaxies, Einstein famously called its inclusion his "greatest blunder," and it was largely ignored for decades. Interest was revived in the late 20th century with the development of inflationary cosmology and, crucially, observations of distant Type Ia supernova by teams like the Supernova Cosmology Project and the High-Z Supernova Search Team.

Theoretical interpretation

In general relativity, the constant represents a repulsive force that acts against gravitational attraction on cosmological scales. Within the framework of quantum field theory, it is naturally identified with the energy density of the vacuum state, arising from quantum fluctuations of fields. This connection leads to a profound theoretical challenge, as naive calculations from quantum electrodynamics and the Standard Model predict a value orders of magnitude larger than observed. The constant's role is central to the Lambda-CDM model, the standard model of Big Bang cosmology, which successfully describes the cosmic microwave background anisotropy measured by missions like WMAP and the Planck (spacecraft).

Observational evidence

The first strong evidence for a positive value came in 1998 from independent observations of Type Ia supernova by the Supernova Cosmology Project led by Saul Perlmutter and the High-Z Supernova Search Team led by Brian Schmidt and Adam Riess. These showed that the expansion of the universe is accelerating, not decelerating. This finding was later corroborated by precise measurements of the cosmic microwave background by the Wilkinson Microwave Anisotropy Probe and the Planck (spacecraft), which constrain the geometry and content of the universe. Additional support comes from studies of baryon acoustic oscillations in large-scale structure surveys like the Sloan Digital Sky Survey and the Dark Energy Survey.

Cosmological constant problem

The central problem is the enormous discrepancy between the observed value, inferred from cosmology, and the theoretical value predicted by quantum field theory. Calculations of vacuum energy from the Standard Model suggest a density roughly 10¹²⁰ times larger than the measured one, a disparity often called the worst theoretical prediction in the history of physics. This fine-tuning issue implies an incredible cancellation of terms, for which no compelling natural explanation exists within established theories. The problem sits at the intersection of general relativity and quantum mechanics, motivating searches for new physics in theories like supersymmetry or string theory.

Alternative explanations

Due to the severe fine-tuning of the constant, many alternative models for dark energy have been proposed. These include dynamical fields like quintessence (physics), a time-evolving scalar field, and modifications to general relativity itself, such as f(R) gravity or Brans–Dicke theory. Other proposals involve the anthropic principle within the context of the multiverse hypothesis, as discussed in frameworks like eternal inflation and the string theory landscape. Ongoing observational programs, such as those conducted by the European Space Agency's Euclid (spacecraft) and the Vera C. Rubin Observatory, aim to distinguish between a true constant and these evolving alternatives.

Category:Physical constants Category:Cosmology Category:General relativity